PHYSICAL REVIEW B 87, 115204 (2013) Lattice contribution to the high dielectric constant of PbTe H. W. Leite Alves and A. R. R. Neto Departamento de Ciˆ encias Naturais, Universidade Federal de S˜ ao Jo˜ ao Del Rei, Caixa Postal 110, 36301-160 S˜ ao Jo˜ ao Del Rei, MG, Brazil L. M. R. Scolfaro * and T. H. Myers Department of Physics, Texas State University, San Marcos, Texas 78666, USA P. D. Borges Instituto de Ciˆ encias Exatas e Tecnologia, Universidade Federal de Vic ¸osa, 38810-000 Rio Paranaiba, MG, Brazil (Received 19 October 2012; published 12 March 2013) The phonon dispersion and the lattice contribution to the dielectric function of PbTe in the NaCl structure are calculated ab initio. The results obtained are in agreement with the available experimental data and reproduce the main features observed in this material, such as an anharmonic LA-TO phonon coupling in the Ŵ-X direction, as well as high values for the dielectric constants ǫ 1 (0) and ǫ 1 (∞). Calculations include the pressure dependence and indicate that the anharmonic phonon coupling is very sensitive to applied pressure. The calculations indicate that the higher values for the dielectric constant together with the anharmonic LA-TO coupling reduce the lattice thermal conductivity and increase the internal electric field, thereby enhancing the electronic conductivity in PbTe, key conditions to increase the thermoelectric figure of merit. DOI: 10.1103/PhysRevB.87.115204 PACS number(s): 72.15.Jf, 63.20.dk, 73.50.Lw, 77.22.Ch Thermoelectric (TE) materials that convert heat flux directly into electrical power are a promising approach to dealing with the challenges of the growing demand for alternative clean energy and are a subject of great scientific interest. The key issue in this area is to develop materials with a significantly increased TE figure of merit, ZT = σS 2 T /κ, where σ is the electrical conductivity, S is the Seebeck coefficient, and κ = κ el + κ latt is the thermal conductivity, composed of the electronic and lattice contributions to thermal conductivity. For practical applications, it is required that ZT ≫ 1. So, a high-quality TE material must have a high electric conductivity, a high thermopower, and a low thermal conductivity. 1 However, in practice, this is hard to achieve for high-conductivity material, as the thermal and electrical conductivity are related by the Wiedemann-Franz law, which states that the Lorenz number L = κ el /σ T is constant. 2 Metals are highly conductive electrically but also have a high thermal conductivity and a low thermopower. For semiconductors, the electronic contribution to the thermal conductivity is much smaller than the lattice contribution and heavily doped semiconductors or semimetals (and their alloys) 3 are the best candidates for TE materials. In this case, understanding the lattice contribution to the thermal conductivity is important to understanding the route to the best TE material. Te-based materials (i.e., PbTe, SnTe, and GeTe) are well-known candidates for medium-temperature TE devices. 4 Besides TE applications, PbTe has also been studied for infrared diodes, 5 spintronics, 6 and optoelectronics, 7 among others. As such, it is a reasonably well-studied material. It is well known that, under ambient conditions, PbTe crystallizes in the B1 (NaCl) structure. Upon the application of a pressure of around 6 GPa, it transforms to an intermediate structure of orthorhombic symmetry (Pnma structure). This intermediate structure then transforms to the B2 (CsCl) modification at 13 GPa. 8,9 From the electronic structure point of view, PbTe is characterized by a small direct semiconducting gap occurring at the L point of the Brillouin zone (BZ). In contrast to most other semiconductors, the band gap of PbTe increases with temperature and decreases under pressure. At the point of gap closure the band dispersions become linear (Dirac type) in the vicinity of the L point. 10–13 Other electronic properties such as effective masses, 10,12 dielectric functions, 11,13 and TE transport properties, 14,15 were also determined. Calculations of lattice dynamics for PbTe have also been well studied by using both semiempirical and first-principles methods, 15–23 resulting in predictions for phonon frequency dispersions, Born effective charges, Gr¨ uneisen parameters, and thermodynamic properties such as heat capacities and Debye temperatures. It is interesting to remark that most results are in good agreement among themselves, as well as with early inelastic neutron scattering (INS) experiments 16 made on PbTe. For example, all calculated phonon dispersions show an LA-TO crossing in the Ŵ-X direction of the BZ. Notable exceptions are the theoretical results of Tian et al., 19 Kong et al., 20 and Bencherif et al. 23 A more recent set of INS experiments 24 suggests that the apparent LA-TO crossing may have been a resolution artifact. In this new experiment (which was done at room and higher temperatures), the development of time-of-flight spectrometers at spallation sources provides the ability to measure the entire four-dimensional scattering function. Using this, Delaire et al. show a signature of a very strong and extended anharmonic LA-TO coupling in their results, which was not observed clearly in the previous lower resolution INS experiments. This LA-TO coupling leads to an avoided-crossing behavior in the dispersions, as well as an 115204-1 1098-0121/2013/87(11)/115204(5) ©2013 American Physical Society